Hướng dẫn sử dụng ROOT cho hệ điều hành Windows

8/13/2019 Hng dn s dng ROOT cho h iu hnh Windows

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Mc lc

Li ni u 4

1 Gii thiu v ROOT 5

1.1 Gii thiu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Lch s hnh thnh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Mt s tnh nng c bn ca ROOT . . . . . . . . . . . . . . . . . . . . . 6

1.4 Cu trc ca ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Cc lp ca ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6 Cch thc ci t v thc thi ROOT . . . . . . . . . . . . . . . . . . . . . 9

1.6.1 Cch ci t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6.2 Cch chy chng trnh trong ROOT . . . . . . . . . . . . . . . . . 10

1.7 Mt s ch khi s dng ROOT . . . . . . . . . . . . . . . . . . . . . . . 121.7.1 Quy c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.7.2 Mt s bin ton cc quan trng . . . . . . . . . . . . . . . . . . . 12

1.8 CINT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.9 ACLiC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.10 Cch bin dch macro. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Kin thc C++ cn bn cho ROOT 15

2.1 Cc lnh xut nhp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Khai bo bin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 Vit nhiu dng lnh mt lc . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Cc php ton. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5 Mt s cu trc iu khin . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.1 Cu trc iu khinif...else... . . . . . . . . . . . . . . . . . . . . . 172.5.2 Cu trc lpfor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.3 Cu trc lpwhile . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5.4 Cc lnh cho vng lp:continuevbreak . . . . . . . . . . . . . . . 18

2.6 Cc lnh dnh cho file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.7 Mng (Array & Vector). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.8 Hm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.9 Con tr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.10 Lp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

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2.11 Bi tp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 Histogram 25

3.1 Khai bo histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Mt s thao tc vi histogram . . . . . . . . . . . . . . . . . . . . . . . . . 253.3 Chng histogram (histogram stack) . . . . . . . . . . . . . . . . . . . . . . 293.4 Histogram 2 chiu v 3 chiu. . . . . . . . . . . . . . . . . . . . . . . . . . 303.5 Profile histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.6 Bi tp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Hm 35

4.1 Khai bo hm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Khai bo hm c cha tham s . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3 Lm khp histogram theo hm. . . . . . . . . . . . . . . . . . . . . . . . . 384.4 TMinuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5 Bi tp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5 th 46

5.1 Canvas v pad. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2 Bng ch gii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.3 Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.4 GraphError . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.5 MultiGraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.6 Cc ty chnh v th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.7 Cch to vn bn v biu thc ton hc . . . . . . . . . . . . . . . . . . . 575.8 Graphics Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.9 Bi tp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6 Cc th vin ton hc 62

6.1 Cc hm ton hc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.2 S ngu nhin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.3 Ma trn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.4 Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.5 Lorentz Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.6 Bi tp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

7 File 72

7.1 Khai bo file. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727.2 Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7.2.1 TNtuple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747.2.2 TTree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

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7.2.3 Cu trc ca tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767.3 Cch to v truy xut d liu t file root . . . . . . . . . . . . . . . . . . . 77

7.3.1 Cch to file root . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777.3.2 Cch truy xut file root . . . . . . . . . . . . . . . . . . . . . . . . 78

7.4 X l s liu c cu trc dng tree . . . . . . . . . . . . . . . . . . . . . . 807.5 Bi tp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Li kt 85

Ti liu tham kho 86

A Cch ci t ROOT cho HH Linux 87

B Bng k hiu mu v marker 89

C K hiu LATEX trong ROOT 90

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Li ni u

Tp ti liu Hng dn s dng ROOT cho h iu hnh Windows c binson nhm mc ch gii thiu cho cc bn trong nhm NMTP v gi phn mm mngun m ROOT, mt trong nhng cng c x l s liu ph bin nht hin nay trongngnh Vt l Ht nhn v Nng lng cao. Mc d y l mt cng c kh thng dng, v ang c s dng trong hu ht cc th nghim ln trn th gii, tuy nhin likh l lm vi cc bn sinh vin chuyn ngnh Vt l Ht nhn ti Vit Nam. Do qua

tp ti liu ny, ti hi vng s gii thiu n cc bn thm mt cng c x l s liu huch na bn cnh cc cng c m cc bn ang s dng nh Origin, Matlab,...

Ni dung ca ti liu tp trung vo nhng vn c bn, ct li nht ca ROOT, cckin thc c trnh by ngn gn v i km cc v d minh ha nhm lm sng t thmvn . Cc ch c la chn trnh by trong ti liu ny l cc vn c bn cnnm vng m tc gi c kt c sau mt thi gian s dng ROOT. Ngoi ra, cuimi phn u c cc bi tp cc bn c th luyn tp vi cc kin thc thu nhn.

Tp ti liu c bin son nhm mc ch trnh by s lc cho cc bn nhng kinthc v k nng c bn nht trong vic s dng ROOT cho cng vic ca mnh. Do, ni dung ca bi vit kh c ng v khng i qu su vo chi tit. c th tmhiu v ROOT mt cch trn vn hn, cc bn c th vo trang web ca ROOT tihttp://root.cern.ch/drupal/;hoc tham gia trao i, tho lun vi cc chuyn gia tihttp://root.cern.ch/drupal/content/roottalk-digest.

ng Nguyn Phng

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Chng 1

Gii thiu v ROOT

1.1 Gii thiu

ROOT l mtframework(th vin cha cc m lnh) dng cho vic phn tch v x l sliu, ch yu cho ngnh Vt l Ht nhn v Ht c bn (Vt l Nng lng cao). Chngtrnh ny c xy dng da trn ngn ng lp trnh C++ vi kh nng lp trnh hngi tng (object-oriented programing).

ROOT c pht trin u tin bi Ren Brun v Fons Rademakers vo gia nhng nm1990 ti T chc Nghin cu Nguyn t Chu u (CERN), v n khong nhng nmu th k 21 n thay th hon ton cho cc framework c xy dng bng ngn ng

Fortran trc ti t chc ny.Mt im c trng d nhn thy nht ca ROOT l vic t chc, sp xp d liudi dng cy (tree) nhm gip cho vic lu tr v x l mt lng ln d liu c hiuqu hn. Hin nay, chng trnh ny ang c s dng trong cc th nghim ti LargeHadron Collider (LHC) v ti hu ht cc th nghim vt l nng lng cao trn th gii.

1.2 Lch s hnh thnh

ROOT c pht trin trong d n th nghim NA49 ti trung tm Nghin cu Nguynt Chu u (CERN). Th nghim ny i hi phi x l mt lng d liu rt ln, khong10 Terabytes/run, do i hi phi pht trin mt th h cng c x l d liu mi thay th cho cng c hin ang c.

Vo gia nhng nm 1990, Ren Brun v Fons Rademakers sau nhiu nm pht trin cccng c x l v m phng cho cc th nghim vt l nng lng cao nh PAW, PIAF,GEANT nhn ra rng cc th vin ngn ng lp trnh Fortran dng nh t ti

gii hn ca n. D cho vn cn rt thng dng, cc cng c ny cn phi c nng cp c th tng thch cho lng d liu khng l ca cc th nghim trong tng lai, c

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CHNG 1. GII THIU V ROOT ng Nguyn Phng

bit l cc th nghim ti Large Hadron Collider (LHC). Cng lc , s pht trin cakhoa hc my tnh c bit l k thut lp trnh hng i tng to tin hxy dng mt cng c da trn nn tng k thut ny.

S pht trin ca ROOT phn ln l nh vo s tng tc ca nhng ngi dng vngi pht trin. V y l m ngun m cho nn bn thn ngi dng cng c th trthnh ngi pht trin bng cch xy dng v tch hp cc m ngun ca mnh vo trongROOT.

T nm 1995 n nay, c rt nhiu phin bn ROOT c ra i:

11/1995: phin bn u tin ROOT 0.5 c cng b

1996: s dng CINT cho ROOT

1997: phin bn ROOT 1.0 1998: phin bn ROOT 2.0

2001: phin bn ROOT 3.0





1.3 Mt s tnh nng c bn ca ROOT

Lu tr d liu:chng ta c th lu tr cc d liu (th hoc qua x l) vthm ch l cc i tng C++ vo trong cc file nn dng .root. Cc d liu clu li di dng cu trc cy (tree) gip cho tc truy xut d liu c tng

ln nhanh chng so vi vic truy xut cc d liu dng thng thng. Truy xut d liu:d liu c lu tr trong cc file root c th c truy xut

t my tnh hoc thng qua mng internet. Vi cc d liu c kch thc ln, ta cth lu tr trn mng grid. Cc d liu c th c chia nh ra nhiu file root khcnhau v c lin kt li trong qu trnh x l.

X l d liu:ROOT l mt th vin ln tp hp rt nhiu cc cng c ton hcv thng k gip chng ta c th x l d liu mt cch tt nht. ROOT cng htr cc x l theo hng lp trnh hng i tng hoc lp trnh song song.

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Trnh by kt qu:cc kt qu c th c trnh by theo rt nhiu dng khcnhau (histogram, chm im, ng,...) v c th c hiu chnh trc tip trnhnh v. Cc hnh v trong ROOT c th c xut ra theo nhiu nh dng khcnhau (pdf, eps, png,...).

M phng:ROOT c kh nng m t cc hnh hc khng gian phc tp, vic mphng trong ROOT c thc hin thng qua cc gi m t hnh hc, tracker vMonte Carlo o.

1.4 Cu trc ca ROOT

Hnh1.1trnh by cu trc ca ROOT. Cc th mc chnh ca ROOT gm c: bin,lib,include,tutorialsvtest.

Hnh 1.1: Cu trc ca ROOT

bin cha cc file thc thi (executable). Mt s file quan trng trong th mc bin:

root.exe:chy root

rootcint:cung cp th vin cc lp cho CINT

rmkdepend:phin bn ca makedependcho ROOT

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root-config:script xc nh cc flag v th vin cho vic bin dch chng trnhc s dng ROOT

cint:chy trnh thng dch C++

makecint:xc nh cc flag v th vin ca rootcint

proofd: chng trnh daemon to user cho qu trnh tnh ton song song bngROOT (PROOF)

proofserv:thc hin tnh ton PROOF

rootd:chng trnh daemon dng iu khin vic truy xut cc file

lib cha th vin chia s (shared object) ca cc lp c nh ngha trong ROOT,ngi dng c th lin kt cc th vin ny vi chng trnh ca mnh. Hnh 1.2 trnhby s ph thuc gia cc th vin vi nhau.

include cha cc file header m t nh ngha ca cc lp.

tutorials cha cc file v d gip ngi dng nm r thm v cc khi nim, k thuttrong ROOT.

test cha cc file v d test framework. Khi mt phin bn mi ca framework cxy dng, cc v d trong th mc ny s c bin dch v thc thi test kh nngca phin bn mi.

Hnh 1.2: S ph thuc ca cc th vin trong ROOT

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1.5 Cc lp ca ROOT

Trong ROOT hin c khong hn 250 lp (class) c chia thnh 11 loi:

Cc lp c bn: bao gm cc lp tng thp nht trong cu trc lp ca ROOT,lm nn tng xy dng nn cc lp khc. VD: TObject, TClass,...

Cc lp lu tr: bao gm cc lp to cu trc d liu (array,list,set,...)

Cc lp histogram:bao gm cc lp histogram 1D, 2D, 3D, cc lp lm khp d liu,hm.

Cc lp ntuple: bao gm cc lp nhTTree, TNtuple,...

Cc lp ha 2D: bao gm cc ha 2D c bn (ng thng, hnh hp, ellipse,...) Cc lp ha 3D: bao gm c khi hnh hc 3D v cc hnh hc detector.

Cc lp giao din ngi dng MOTIF: cha cc thnh phn giao din tng t nhcc cng c khc nh ca s, nt bm, menu,...

Cc lp giao din tng tc: cha cc ng dng tng tc, trnh thng dch C++.

Cc lp tng tc vi h iu hnh: cc lp tng tc vi h iu hnh thng quaTSystem(TUnixSystem, TWinNTSystem, TMacSystem).

Cc lp mng (network): cc ng dng xy dng h thng mng.

Cc lp ti liu: cho php to cc ti liu (dng HTML), file header v sourceC++,...

1.6 Cch thc ci t v thc thi ROOT

1.6.1 Cch ci t

ROOT l gi phn mm m ngun m min ph, c th c download ti trang webhttp://root.cern.ch/drupal/,thch hp cho rt nhiu h iu hnh nh Linux, Windows,Mac OS,...

Trong phn ny tc gi ch trnh by cch thc ci t ROOT cho h iu hnh Windows,cn cch ci t cho h iu hnh Linux c trnh by trong phn Ph lc A. i vicho h iu hnh Windows, cch thc n gin nht ci t ROOT l ci t thng

file binary ca chng trnh ny, cc bc tin hnh nh sau:

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Download ROOT ti:http://root.cern.ch/drupal/content/downloading-root, nhp chn version cndownload (Hnh1.3).

ng vi mi version s c nhiu file source khc nhau cho mi h iu hnh, chnfile c ui.msicho h iu hnh Windows (Hnh1.4).

Double click vo file download v ci t nh nhng chng trnh bnh thng.

Hnh 1.3: Cc phin bn ca ROOT

Hnh 1.4: File download

1.6.2 Cch chy chng trnh trong ROOT

khi ng ROOT, ta c th thc hin 1 trong 2 cch sau:

Cch 1:double click vo biu tng ROOT c to ra sau khi ci t.

Cch 2:m ca sCommand Prompt, g lnhroothocroot -l.

G lnh.q thot ra khi ROOT.

thc thi cc lnh, ta c th g cc lnh ny trc tip ti du nhc lnh ca ROOThoc to mt file macro v chy file ny ti du nhc lnh ca ROOT. Thng thng cc

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Hnh 1.5: Giao din khi khi ng ca ROOT

file macro c s dng trong ROOT l cc file C++, cho nn thng c ui dng nh.c,.cpphoc.cxx. Cc lnh trong file macro c bao li bi mt cp ngoc nhn {}.

V d:to mt file macroten.cxxyu cu ngi dng nhp vo tn ca mnh:

{

Char_t ten[ 1 0 0 ] ;

cout


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Ngoi ra ta cng c th gi thc thi macro ngay t bn ngoi ROOT bng cch g lnhnh sau

$ r oo t t en.cxx

Trong trng hp thc thi macro, nu file macro c cha nhiu hm bn trong, ta cnt tn hm chnh trong file trng vi tn ca file.

1.7 Mt s ch khi s dng ROOT

Trong phn ny ti s trnh by mt s quy c k hiu v nhng iu cn lu trongROOT cc bn c th d dng theo di v nm bt ngha ca cc v d nhngphn sau.

1.7.1 Quy c

Cc quy c k hiu trong ROOT gm c:

Cc lp bt u bng k tT, v d nhTH1, TTree,...

Cc khai bo khng thuc lp c kt thc bng _t, v d nhInt_t, Float_t,...

Cc thnh phn ca d liu c bt u bng k tf, v d nhfTree,...

Cc hm, lnh trong lp c bt u bng k t hoa, v d nhLoop(),Integral(),...

Cc hng s c bt u bng k tk, v d nhkRed, kInitialSize,...

Cc bin ton cc c bt u bng k tg, v d nhgEnv, gSystem,...

Cc thnh phn tnh ca d liu c bt u bng k tfg, v d nhfgTokenClient,...

Cc bin cc b v tham s c bt u bng k t thng, v d nhnbytes,...

Cc lnh, hm gn gi tr v truy xut gi tr c bt u bng cc tSetvGet,v d nhSetLast(), GetFirst(),...

1.7.2 Mt s bin ton cc quan trng

gROOTlu gi thng tin ca hin ti trong ROOT, bng cch s dng gROOTtac th truy cp ti tt c cc i tng ang c to ra trong ROOT.

gSystemtng tc vi h iu hnh.

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gFiletr n file ang m trong ROOT.

gDirectorytr n th mc ang lm vic.

gPadtr n pad ang hot ng.

gRandomtr n b phn pht s ngu nhin ang hot ng.

gEnvcha tt c cc thit lp mi trng trong qu trnh s dng ROOT.

V d:

root [ 0 ] gROOT>Reset ( ) ;

root [ 1 ] gSystem>Load ( " . . / l i b /libQFramework . so" ) ;

root [ 2 ] gStyle>SetFrameBorderMode ( 0 ) ;

1.8 CINT

CINT l mt trnh thng dch C++ c to bi Masa Goto, v c tch hp trongROOT thng dch cc lnh C++ do ngi dng to ra. Trnh thng dch ny c nhimv c v thc thi tng cu lnh do ngi dng to ra, nhng khng bin dch thnhngn ng my. Mc d vic ny lm cho tc chy mt chng trnh thng dch chm

hn rt nhiu so vi mt chng trnh c bin dch, tuy nhin vic ny s thun tinhn cho ngi dng trong trng hp phi chnh sa m ngun nhiu ln do thi gianbin dch lu hn nhiu so vi thi gian thng dch.

Mc d c tch hp trong ROOT nhng CINT l mt chng trnh c lp v c thdownload ti http://root.cern.ch/drupal/content/cint.

Cch vit nhiu dng lnh

Cc cm dng lnh bt u v kt thc bng cp ngoc nhn {}

Cc lnh bn trong kt thc bng du ;

Tt c cc i tng c to ra l ton cc

1.9 ACLiC

ACLiC (Automatic Compiler of Libraries for CINT) l trnh bin dch c nhim v to

ra cc th vin chia s da trn m ngun C++ do ngi dng vit ra, s dng cc tychnh c thit lp tng t nh khi thc thi ROOT.

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Cch bin dch macro vi ACLiC c th bin dch c cc macro vi ACLiC,iu u tin l chng ta cn khai bo thm cc file header ph hp vo trong script camacro (iu ny l khng cn thit i vi CINT).

V d: to ra cc th vin chia s, ta thm du +vo sau tn file macro khi load, chng hnnh

root [ 0 ] . L t en.cxx+

Chng trnh s bin dch v to ra cc file chia s c ui .so. V d nh file macro cachng ta c tn lmacro1.cxxth file th vin to ra s c tn l macro1_cxx.so

1.10 Cch bin dch macro

bin dch macro thnh mt chng trnh c lp (stand alone) chng ta cn phi bindch vi mt trnh bin dch C/C++, trong trng hp ny chng ta s s dng g++.Trc khi bin dch, cn phi chc chn l tt c cc file header cn thit u cinlcude. lm c iu , chng ta s dng cng c root-config, y l mt scriptca ROOT cung cp tt c cc flag v th vin cn thit c th bin dch c chngtrnh v lin kt chng ti cc th vin ca ROOT. Lu rng c th to ra mt

chng trnh c lp, chng ta cn khai bo hmmain()trong code. Hm main()c thc to ra ch vi mt nhim v duy nht l gi hm macro.

V d:

# i f n d e f __CINT__

i n t main ( ) {

Macro ( ) ;

r e t u r n 0 ;

}

# e n d i f

Khi chy chng trnh trong ROOT,__CINT__c xc nh th on code trn s khngc thc thi, ngc li khi bin dch vi g++CINT khng c xc nh th on codetrn s c thc thi.

bin dch mt chng trnh c lp t fileMacro.Cta ch cn g on lnh:

g++ o M ac ro.exe Macro. C rootconfig cflags libs

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Chng 2

Kin thc C++ cn bn cho ROOT

ROOT l mt framework c xy dng trn nn tng ngn ng lp trnh C/C++, do mt s kin thc v lp trnh C/C++ l cn thit c th s dng c ROOT.

Trong phn ny, ti s trnh by mt s im chnh ca ngn ng lp trnh C++ bsung kin thc nn tng cho vic s dng ROOT trong nhng phn sau. Nu cc bn c kin thc v lp trnh C++ trc ri th c th b qua phn ny m i thng vonhng phn sau.

2.1 Cc lnh xut nhp

cin,cout: cc lnh nhp, xut d liu trn mn hnh. endl: lnh kt thc dng v xung dng mi.

V d:

root [ 0 ] cout


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CHNG 2. KIN THC C++ CN BN CHO ROOT ng Nguyn Phng

2.3 Vit nhiu dng lnh mt lc

Trong ROOT, c th vit c nhiu dng lnh cng mt lc, ta s dng cp ngoc

nhn {} m u v kt thc cc dng lnh.V d:

root [ 0 ] {

end with ' } ' , '@ ':abort > I nt _t x = 0 , y = 3 ;

end with ' } ' , '@ ':abort > x = y 2 ;

end with ' } ' , '@ ':abort > cout = so snh ln hn hoc bng


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ln(x) hm logarit t nhin

V d:

root [ 0 ] I n t_ t x=3 ; // x = 3

root [ 1 ] cout


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2.5.3 Cu trc lp while

Cu trc:while (iu kin) { cc lnh thc thi }

hocdo { cc lnh thc thi } while (iu kin)

V d:

root [ 0 ] I n t_ t x=5 ; do { cout


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close(),open(): lnh ng, m file.

V d:

root [ 0 ] ofstream f ( " f i l e . tx t " ) ; / / Mo mot f i l e c o t e n l a f i l e . t x t

d e g h i d u l i e uroot [ 1 ] f


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( Int_t ) 3

Ngoi ra, con tr cng c s dng trong khai bo mt mng, hm hay file.

V d:khai bo mt mng cha bin kiu s nguyn, a ch ca con tr tr ti cng chnhl a ch ca phn t u tin trong mng

root [ 0 ] Int_t a ;

2.10 Lp

Lp (class) l mt kiu d liu do ngi dng t nh ngha, c th bao gm trong n ccd liu v hm. Cch thc khai bo mt lp nh sau:

class {

:

d liu 1;

d liu 2;

hm 1;

....

} ;

Thuc tnh ca d liu v hm c cc dng: private(ch c truy xut bi cc thnhvin trong cng lp),protected(c th c truy xut bi cc thnh vin trong cng lphoc t cc lp k tha), hoc public(c th c truy xut t bn ngoi lp).

V d:

c l a s s Sinhvien { // Tao mot lo p co t en l a S i nh v ie n

p u b l i c:

Char_t ten[ 1 0 0 ] ;

Int_t tuoi;

Int_t diemthi;

Sinhvien ( ) {} / / C o n s t r uc t o r

~Sinhvien ( ) {} / / D e s t ru c t o r

v o i d ketqua ( ) {

i f( diemthi >= 5)

cout


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Bng 2.1: Cc trng s bc x WrLoi bc x v nng lng WrPhoton 1Electron & muon 1Neutron di 10 keV 5Neutron t 10 keV n 100 keV 10Neutron t 100 keV n 2 MeV 20Neutron t 2 MeV n 20 MeV 10Neutron trn 20 MeV 5Proton trn 2 MeV 5Ht , ion nng 20

Bng 2.2: Cc trng s m Wt

M/C quan Wt M/C quan WtTuyn sinh dc 0.20 V 0.05Ty ca xng 0.12 Gan 0.05Rut kt 0.12 Thc qun 0.05Phi 0.12 Tuyn gip 0.05D dy 0.12 Da 0.01Bng quang 0.05 B mt xng 0.01Cc m cn li 0.05

nh theo cng thc bn thc nghim Weizsacker:

EB(A, Z) = av A +as A2/3 +ac

Z2

A1/3+aa

(N Z)2

4A +

A1/2

viN =A Z, av= 15.7 MeV, as= 17.2 MeV, ac= 0.7 MeV, aa= 93.2 MeV v= 0 nu A l,11.2 MeV nu Z v A cng chn, +11.2 MeV nu Z v A cng l.Vit chng trnh:

Yu cu ngi dng nhp vo s khi A v lit k ra cc ng v bn c cng

s khi A . Yu cu ngi dng nhp s nguyn t Z v s khi A, xc nh l ng v

no, c bn hay khng, nu khng bn th s phn r pht , + hay.

Bng danh sch cc nguyn t c lit k trong fileelement_list.txt, c downloadti http://nmtp.wikispaces.com/file/detail/element_list.txt.

5. Download file ph Uranium c o bng detector HPGe 8192 knh ti http://nmtp.wikispaces.com/file/detail/Uranium.tka,file ny c th m c di

dng text. To mt lp c tn l Pho cha cc thnh phn:-tenfile: cha tn ca file ph.

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http://nmtp.wikispaces.com/file/detail/element_list.txthttp://nmtp.wikispaces.com/file/detail/element_list.txthttp://nmtp.wikispaces.com/file/detail/Uranium.tkahttp://nmtp.wikispaces.com/file/detail/Uranium.tkahttp://nmtp.wikispaces.com/file/detail/Uranium.tkahttp://nmtp.wikispaces.com/file/detail/Uranium.tkahttp://nmtp.wikispaces.com/file/detail/Uranium.tkahttp://nmtp.wikispaces.com/file/detail/element_list.txt


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Chng 3

Histogram

Theo nh ngha thng thng, histogram l mt dng biu phn b ca mt ilng no . Trong ROOT, lp histogram c k hiu l THdp, vi dl s chiu ca

histogram v pl kiu ca cc phn t cha trong histogram (tham kho thm ti ftp://root.cern.ch/root/doc/3Histograms.pdf). Cc li histogram chnh trong ROOTgm c: 1D, 2D, 3D v profile.

V d:TH1Fl lp histogram 1 chiu (1D), cc phn t trong histogram s c kiu s thc(float).

3.1 Khai bo histogram

Ta c th khai bo mt histogram theo c php nh sau:

* = new ("", "", , , );

V d:

root [ 0 ] TH1F h = new TH1F ( "h", " Pho gamma", 8 19 2 , 0 , 8 19 2) ;

V d trn khai bo 1 histogram tn l h c tiu l "Pho gamma" vi s khong chial 8192 khong (bin), rng mi khong chia l 1.

3.2 Mt s thao tc vi histogram

Sumw2(): thc hin lu tr tng bnh phng cc trng s i km vi cc gi tr cahistogram trong qu trnh ghi nhn (nn gi ngay sau khi khai bao histogram)

root [ 1 ] h>Sumw2 ( ) ;

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ftp://root.cern.ch/root/doc/3Histograms.pdfftp://root.cern.ch/root/doc/3Histograms.pdfftp://root.cern.ch/root/doc/3Histograms.pdfftp://root.cern.ch/root/doc/3Histograms.pdf


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CHNG 3. HISTOGRAM ng Nguyn Phng

Fill(x): tng 1 s m ti v tr tng ng vi gi tr a vo

root [ 1 ] h>Fill ( value ) ;

Fill(x, w): tng 1 s m vi trng swti v tr tng ng vi gi tr a voroot [ 1 ] h>Fill ( value,weight ) ;

SetBinContent(i, x): gn gi tr tng ng vi v tr ca khong chia

root [ 1 ] h>SetBinContent ( i ,value ) ;

GetBinContent(i): ly gi tr tng ng vi v tr ca khong chia

root [ 1 ] h>GetBinContent ( i ) ;

Integral(): tnh tch phn histogram

root [ 1 ] h>Integral ( ) ; / / t i nh t i c h phan tu b in 1 d en b in c uo i

root [ 2 ] h>Integral ( i , j ) ; // t in h t i ch phan tu bi n i den bin j

root [ 3 ] h>IntegralAndError ( i , j ,er r ) ; // t i nh t i c h phan tu b in

i den b in j , s a i s o thong ke cua t i c h phan duoc l uu vao t ro ng

e r r

Draw(): v histogramroot [ 1 ] h>Draw ( ) ;

V d:(xem Hnh3.1)

{

// Tao h is to gr am c o 5 khoang c h ia t u 0 den 5

TH1F h = new TH1F ( "h", "", 5 , 0 , 5 ) ;

h>Fill ( 1 ) ; / / T ang 1 s o dem t a i khoang c h ia t u 1 den 2

h>Fill ( 3 ) ; / / T ang 1 s o dem t a i khoang c h ia t u 3 den 4h>Fill ( 3 ) ; / / T ang 1 s o dem t a i khoang c h ia t u 3 den 4

h>Fill( 4 . 3 ) ; / / T ang 1 s o dem t a i khoang c h i a t u 4 den 5

h>Draw ( ) ; / / Ve h i s t og r a m

}

Truy xut cc thng s ca histogram:

GetEntries(): s lng cc gi tr c ghi nhn trong histogram

GetMean(), GetMeanError(): gi tr trung bnh v sai s tng ng GetRMS(), GetRMSError(): cn ca phng sai v sai s tng ng

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Hnh 3.1: Biu ca v d

GetMaximum(), GetMinimum(): gi tr ln nht v nh nht trong histogram

GetMaximumBin(), GetMinimumBin(): ly v tr bin tng ng vi gi tr ln nhtv nh nht

GetBinCenter(i): gi tr trung tm ca bin th i

V d:S dng v d trong Hnh3.1

root [ 0 ] cout


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h1>SetFillColor ( kRed ) ;

/ /Tao h i s t og r a m h2 ba ng c a ch g i e o n ga u n h i en ham e x p o n e n t i a l

TH1F h2 = new TH1F ( "h2", " H i s to g r am 2 ", 1 00 ,4 , 4 ) ;

h2>FillRandom ( "expo", 1 0 0 0 0 ) ;

h2>SetFillColor ( kBlue ) ;

/ / Them h a i ham v ao s t a c k

hs>Ad d ( h1 ) ;

hs>Ad d ( h2 ) ;

/ / Ve h i s t og r a m

/ / hs>Draw ( " n o s t a c k " ) ; / / v e k ho ng x ep c ho n g

hs>Draw ( ) ; / / v e x ep ch on g

}

Hnh 3.3: V d v xp chng histogram: hnh bn tri l hai histogram v trn cng th, hnh bn phi l hai histogram c xp chng ln nhau.

3.4 Histogram 2 chiu v 3 chiu

Tng t nh vi histogram 1 chiu

V d:Histogram 2 chiu (xem Hnh3.4)

{

TH 2 h2 = new TH2D ( "h2", " 2 D h i s t o g r a m ",1 00 ,0 ,70 ,10 0 ,0 ,200 00) ;

Double_t x , y ;

f o r ( I nt _t i = 0 ; i < 1 0 0 0 0 ; i++) {

// G ieo ngau n hi en c ac g i a t r i x , y t he o ham G auss

x=gRandom>Gaus ( 4 0 , 1 0 ) ;

y=gRandom>Gaus ( 1 0 0 0 0 , 3 0 0 0 ) ;

h2>Fill ( x , y ) ;}

h2>Draw ( " c o l " ) ;

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}

Hnh 3.4: V d histogram 2 chiu

V d:Histogram 3 chiu (xem Hnh3.5)

{

TH3D h3=new TH3D ( "h3", " 3 D h i s t o g r a m ",2 0 , 2 ,2 ,20 , 2 ,2 ,2 0 ,0 ,4 ) ;Double_t x , y , z ;

f o r ( I nt _t i =0 ; i Gaus (2 ,2) ;

y=gRandom>Gaus (2 ,2) ;

z=xx+yy ;

h3>Fill ( x , y , z ) ;

}

h3>SetFillColor ( kCyan ) ;h3>Draw ( " i s o " ) ;

}

3.5 Profile histogram

Profile histogram nhm gip cho ngi dng thy c s tng quan gia cc bin vi

nhau trong cng mt histogram (2 chiu hoc 3 chiu). Trong mt s trng hp, ccprofile c th c xem l s biu din thay th cho cc th histogram nhiu chiu.

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Hnh 3.6: V d profile 1 chiu

}

hprof2d>Draw ( ) ;

}

Hnh 3.7: V d profile 2 chiu

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3.6 Bi tp

1. Mt ngun phng x A c hot phng x nm 2000 l 1.2 mCi, v th biu

din hot ca ngun ny theo tng nm trong khong thi gian t nm 2000n 2020, bit chu k bn r ca ngun ny l 8 nm.

2. Mt sinh vin tin hnh th nghim o s m ghi nhn c theo khong ccht v tr ng n ngun. S m ghi nhn c theo khong cch c trnh bytrong Bng3.1, v th phn b s m theo khong cch v c lng s mghi nhn c ti khong cch d = 1.8m.

Bng 3.1: S m theo khong cch

Khong cch (m) 1 1.2 1.5 2 2.5S m 541 353 169 42 8

3. S dng file ph phng x o c tihttp://nmtp.wikispaces.com/file/detail/pho_do.tkav phng nn ti http://nmtp.wikispaces.com/file/detail/phong_nen.tka,ghi cc s m ca hai ph ny vo cc histogram tng ng.

Xc nh v tr knh c s m ln nht, nh nht ca ph o.

V cc histogram ca ph o, phng nn v ph o tr cho phng nn trncng 1 th. Gi : v mt histogram trn cng th vi histogram c v trc , ta thm option same vo trong lnh vDraw("same")

Tnh din tch nh sau khi tr phng.

34
http://nmtp.wikispaces.com/file/detail/pho_do.tkahttp://nmtp.wikispaces.com/file/detail/pho_do.tkahttp://nmtp.wikispaces.com/file/detail/phong_nen.tkahttp://nmtp.wikispaces.com/file/detail/phong_nen.tkahttp://nmtp.wikispaces.com/file/detail/phong_nen.tkahttp://nmtp.wikispaces.com/file/detail/phong_nen.tkahttp://nmtp.wikispaces.com/file/detail/phong_nen.tkahttp://nmtp.wikispaces.com/file/detail/pho_do.tkahttp://nmtp.wikispaces.com/file/detail/pho_do.tka


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Chng 4

Hm

Trong ROOT, lp hm (function) c k hiu l TFd, vi dl s chiu ca ca hm. Vd TF1l lp hm 1 chiu, TF2l lp hm 2 chiu,...

4.1 Khai bo hm

C php chung cho vic khai bo mt hm l:

* = new ("", "", , );

Ta c th khai bo cng thc ca mt hm theo 1 trong 3 cch sau:Cch 1:to trc tip mt hm da vo cc cng thc C++ c sn

V d:Khai bo hm sin(x)/x (xem Hnh4.1)

root [ 0 ] TF 1 f = new TF 1 ( " f ", " s i n ( x ) / x", 0 , 1 00 )

root [ 1 ] f>Draw ( )

Cch 2:to trc tip mt hm da vo lp TMath

V d:Khai bo hm Gaussian cx= 50 v= 5.3 (xem Hnh4.2)root [ 0 ] TF 1 f = new TF 1 ( " f ", " [ 0 ] TMath : : Gaus ( x ,5 0 , 5. 3 ) ", 0 , 2 00 )


Cch 3:t nh ngha hm ring

V d:Khai bo hm x2 + x + 1 = 0 (xem Hnh4.3)

Double_t my_func ( Double_t x ) {

r e t u r n ( xx+x+1);

}

root [ 0 ] TF 1 f = new TF 1 ( " f ", "my_func(x)", 0 , 1 0 0)

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CHNG 4. HM ng Nguyn Phng

Hnh 4.1: th ca hm sin(x)/x

Hnh 4.2: th ca hm Gauss(50,5.3)


4.2 Khai bo hm c cha tham s

Trong trng hp khai bo cc hm c tham s, k hiu ca cc tham s c t trong cpngoc vung []. Gi tr ca cc tham s c th c gn thng qua hm SetParameter()

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4.3 Lm khp histogram theo hm

lm khp histogram, ta c th dng lnh Fit()(xem thm ti http://root.cern.

ch/root/HowtoFit.htmlvhttp://root.cern.ch/root/html/TH1.html#TH1:Fit) vic php sau:

>Fit(, ,... )

i vi mt s hm c bit, ta ch cn khai bo t kha m khng cn phi khai bohm:

gaus: hm Gaussian vi 3 tham s, f(x) = [0]*exp(-0.5*((x-[1])/[2])**2)

expo: hm e m vi 2 tham s, f(x) = exp([0]+[1]*x)

polN: hm a thc bc N, f(x) = [0] + [1]*x + [2]*x**2 + ...

Mt s option thng c s dng khi lm khp:

W: chuyn tt c trng s ca cc bin khc 0 v 1.

WW: chuyn tt c trng s ca cc bin v 1.

L: s dng phng php log likelihood.

U: s dng phng php lm khp do ngi dng t nh ngha.

V: s dng verbose mode.

E: s dng k thut Minos trong c lng sai s.

0: khng v kt qu lm khp.

V d: Gieo s ngu nhin phn b dng Gauss v lm khp li theo dng ny (xemHnh4.5)

{

TH1F h = new TH1F ( "h", " G a u s s i a n ",1 00 ,0 ,20 0) ;Float_t mean = 1 0 0 , sigma = 2 0 ;

f o r ( I nt _t i = 0 ; i < 1 0 00 ; i++) { // g i e o ngau n hi en 1 00 0 l a n

h>Fill ( gRandom>Gaus (mean ,sigma ) ) ; // g i e o ngau n hi en t he o

phan bo Gauss

}

TF 1 f = new TF 1 ( " f ", " [ 0 ] TMath : : Gaus( x , [ 1 ] , [ 2 ] ) ", 0 , 2 00) ;

f>SetParameters (10 ,10 ,10 ) ;

h>Fi t ( " f " ) ; // t a c o t he su dung f >F i t ( " g a u s " ) t ha y t h e

h>Draw ( ) ; // ve h is to gr am h

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f>Draw ( "same" ) ; / / v e ham lam k hop f t r e n c un g do t h i

}

Kt qu lm khp nh sau:

FC N =65.1586 FROM MIGRAD STATUS=CONVERGED 35 8 CALLS 35 9

TOTAL

ED M =4.68058 e009 STRATEGY= 1 ERROR MATRIX

ACCURATE

EXT PARAMETER STEP FIRST

NO . NAME VALUE ERROR SIZE DERIVATIVE

1 p0 3 . 6 3 1 3 2 e+001 1 . 5 26 2 3 e+000 4 . 7 17 0 9e003 6 . 14 78 9 e005

2 p1 1 . 0 0 2 6 2 e+002 6 . 9 49 9 8e001 2 . 76 0 13 e003 9.82112 e007

3 p2 2 . 0 6 8 2 6 e+001 5 . 7 60 7 8e001 1 . 78 0 36 e003 2 . 12 47 0 e004

Hnh 4.5: th lm khp hm dng Gauss

Trong trng hp mun c nh 1 tham s trong qu trnh lm khp, ta c th s dnglnh FixParameter, v d

f>FixParameter( 0 , 1 . ) ;

Ngoi ra ta cng c th xc nh khong lm khp

h>Fi t ( " f ", " ", " ",40 ,160 ) ;

Cc tham s lm khp c th c truy xut qua cc lnh sau: GetFunction("f"): ly hm c lm khp

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GetChisquare(): gi tr 2 ca vic lm khp

GetParameter(i): gi tr ca tham s th i

GetParError(i): sai s ca tham s th i

V d:

root [ 1 ] f>GetChisquare ( )

(c o n s t Double_t ) 6 . 5 1 5 8 5 9 7 6 9 2 8 2 9 4 1 7 0 e+001

root [ 2 ] f>GetParameter ( 1 )

(c o n s t Double_t ) 1 . 0 0 2 6 1 6 3 4 2 8 3 0 9 2 4 5 0 e+002

root [ 3 ] f>GetParError ( 1 )

(c o n s t Double_t ) 6 . 9 4 9 9 7 6 4 1 7 1 9 1 0 3 6 1 0 e001

V d:Lm khp s liu vi nh Gaussian v phng nn a thc bc 2 (xem Hnh4.6)

/ / Ham mo t a p ho ng n en d an g d a t h u c b ac 2

Double_t background ( Double_t x , Double_t pa r ) {

r e t u r n pa r[ 0 ] + pa r[ 1 ] x[ 0 ] + pa r[ 2 ] x [ 0 ] x[ 0 ] ;

}

/ / Ham mo t a d i n h d an g G a u ss i a n

Double_t Gaussian ( Double_t x , Double_t pa r ) {

r e t u r n ( pa r[ 0 ] TMath: : Gaus ( x[ 0 ] ,par [ 1 ] ,par [ 2 ] ) ) ;}

/ / Ham l am k ho p b an g t o n g c ua ham d i n h G a u ss i a n v a p ho ng n en

Double_t function ( Double_t x , Double_t pa r ) {

r e t u r n background ( x ,pa r ) + Gaussian ( x ,& pa r[ 3 ] ) ;

}

/ / Thuc h i e n v i e c lam kho p

v o i d fitting ( ) {c on st i n t nBins = 5 0 ;

Double_t data[nBins] = { 1 5 , 2 2 , 2 5 , 1 8 , 2 2 , 2 2 , 1 6 , 2 1 , 1 9 ,

20 ,34 ,41 ,45 ,49 ,7 2 ,77 ,91 ,89 ,

90 ,94 ,96 ,94 ,84 ,8 0 ,64 ,61 ,52 ,

38 ,39 ,31 ,32 ,24 ,2 5 ,25 ,30 ,20 ,

27 ,20 ,20 ,14 ,16 ,18 ,1 2 ,23 ,

8 ,22 ,17 ,12 ,23 ,12 };

TH1F h = new TH1F ( "h", "Gaus s ian + backgr ound",5 0 ,0 , nBins ) ;

f o r(i n t i=0 ; i < nBins; i++) {

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h>SetBinContent ( i+1 , data[ i] ) ;

}

h>Sumw2 ( ) ;

/ / t a o ham TF1 t u 0 den n Bi ns , c o 6 tham s o ( 3 c ho phong nen , 3 c ho

d i n h )

TF 1 f = new TF 1 ( " f ", function , 0 , nBins, 6 ) ;

/ / dua tham s o da u v ao

f>SetParameter ( 4 , 2 0 ) ; // u oc l uo ng v i t r i dinh

f>SetParameter ( 5 , 1 0 ) ; // uoc l uo ng be ro ng d in h

h>Fi t ( " f " ) ;

/ / k ha o b ao ham r i e n g c ho ph on g n e n va d i nh

TF 1 bk g = new TF 1 ( "bkg", background , 0 , 5 0 , 3 ) ;

bkg>SetLineColor ( 3 ) ;

TF 1 peak = new TF 1 ( "peak", Gaussian, 0 , 5 0 , 3 ) ;

peak>SetLineColor ( 4 ) ;

Double_t par[ 6 ] ;

/ / dua c a c tham s o v ao ham p ho ng n en va d i nh s a u do v e c a c ham n ay

f>GetParameters ( pa r ) ;

bkg>SetParameters ( pa r ) ;

bkg>Draw ( "same" ) ;

peak>SetParameters (&pa r[ 3 ] ) ;

peak>Draw ( "same" ) ;

}

4.4 TMinuit

Minuit l mt gi lm khp bng phng php cc tiu ha hm mc tiu (objectivefunction) nm trong PACKLIB, c vit u tin bng ngn ng lp trnh Fortran biFred James v c chuyn sang lp TMinuitbng ngn ng C++ bi Rne Brun. Chiv lp ny c th c xem ti http://root.cern.ch/root/html/TMinuit.html.

Cc bc tin hnh lm khp s dng lp TMinuit

Xy dng hm cc tiu ha "FCN" (chi square, likelihood,...).

Khai bo d liu lm khp.

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Hnh 4.6: Lm khp s liu vi dng nh Gaussian v phng nn a thc bc 2

Khai bo i tng thuc lp TMinuit lm khp, cc tham s v khong lmkhp, cng vi cc kiu lm khp

SIMPLEX: tm cc tiu a phng, u im ca phng php ny l tc nhanh, tuy nhin chnh xc khng cao lm.

MIGRAD: lm khp hm a phng s dng phng php Davidson-Fletcher-Powell ci tin.

HESSE: tnh ma trn o hm bc hai ca hm FCN s dng phng php viphn hu hn (finite difference method), thng c s dng ti u ktqu thu c tMIGRAD.

MINOS: phn tch sai s (bt i xng), thng thng ta hay s dng t nhthai phng php (HESSEc s dng ngay sau MIGRAD). Cn MINOSc s

dng ti u sai s ca cc gi tr lm khp. Tr v kt qu lm khp (cng vi cc kim tra thng k).

V d:

Float_t z[ 5 ] ,x[ 5 ] ,y[ 5 ] ,errorz[ 5 ] ;

//_________________________________________________________________

v o i d fc n ( Int_t &npar, Double_t gin, Double_t &f , Double_t par,

Int_t iflag )

{

c o n s t Int_t nbins = 5 ;

I nt _t i ;

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/ / Tinh c h i s q u a r e

Double_t chisq = 0 ;

Double_t delta;

f o r ( i=0 ;i


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Chng 5

th

5.1 Canvas v pad

Canvasl mt ca s m hnh nh c th c hin th trn . Mt canvas c th cchia thnh 1 hay nhiu khu vc v, cc khu vc v ny c gi l pad.

Trong ROOT, nu canvas khng c khai bo trc khi v hnh, chng trnh s mcnh to ra canvas c tn lc1, v pad tng ng cng c cng tn vi canvas ny. Mtpad c th nm trong 1 canvas hoc nm trong 1 pad khc.

C php khai bo canvas nh sau:

TCanvas * = new TCanvas("", "", , )

hoc

TCanvas * = new TCanvas("", "", form)

vi form = 1 kch thc 700 500ti (10,10)form = 2 kch thc 500 500ti (20,20)form = 3 kch thc 500 500ti (30,30)form = 4 kch thc 500 500ti (40,40)form = 5 kch thc 500 500ti (50,50)

C php khai bo pad nh sau:

TPad * = new TPad("", "", xlow, ylow, xup, yup, color,

bordersize, bordermode)

Trong :xlow v tr ca im di bn tri ca pad ang khai boylow ta y ca im xup v tr ca im trn bn phi ca pad ang khai boyup ta y ca im

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CHNG 5. TH ng Nguyn Phng

color k hiu mu ca pad (xem Ph lcB)bordersize kch thc bin ca pad (tnh theo pixel)bordermode hiu ng bin chm xung (=1)bordermode khng c hiu ng (= 0)bordermode hiu ng bin ni ln (= 1)

Mt s lnh lin quan n canvas v pad:

(xem thm tihttp://root.cern.ch/root/html/TPad.htmlvhttp://root.cern.ch/root/html/TCanvas.html)

Divide(nx,ny): chia canvas/pad ra lm nhiu phn theo trc x v y, cc pad nhbn trong s c nh s t 1 n nx*ny

cd(i): chn pad nh th i, mc nh cd() = cd(0) tc l chn chnh canvas/pad

GetPad(i): chn pad th i (trng hp nm trong mt pad khc)

SetCanvasSize(w,h): chnh kch thc cho canvas

SetBorderSize(): chnh kch thc cho bin

SetBorderMode(): chnh kiu cho bin

SetLogx(), SetLogy(), SetLogz(): v trc x,y,z theo thang log

SetGrid(), SetGridx(), SetGridy(): v li cho trc ta

SetTicks(), SetTickx(), SetTicky(): nh du cc khong chia cho trc ta

Print("file"): lu ni dung trong hnh v ra file

SaveAs("file"): tng t Print

V d 1:(xem Hnh5.1)

{

TH1F h1 = new TH1F ( "h1", "1D Gaus s ian", 1 00 , 1 00 , 1 0 0 ) ;

TH2F h2 = new TH2F ( "h2", "2D Gaus s ian", 100 ,100 , 1 00 , 1 00 , 100,100 ) ;

h1>Sumw2 ( ) ;

h2>Sumw2 ( ) ;

Float_t mean = 0 , sigma = 2 0 ;

f o r ( I nt _t i = 0 ; i < 1 0 0 0 0 ; i++) {

h1>Fill ( gRandom>Gaus (mean ,sigma ) ) ;

h2>Fill ( gRandom>Gaus (mean ,sigma ) , gRandom>Gaus (mean ,sigma ) ) ;

}

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Lu :trong mt s trng hp sau khi s dng lnhDraw(), nu bng ch gii (thm chl trc ta ) khng hin th nh c chnh sa th nn g thm lnhgPad->RedrawAxis()sau khi chnh sa.

V d:So snh 2 dng phn b Gauss v Landau (xem Hnh5.3){

TH1F h1 = new TH1F ( "h1", " So s a nh ", 5 0 , 0 , 1 0 0 ) ;

TH1F h2 = new TH1F ( "h2", " So s a nh ", 5 0 , 0 , 1 0 0 ) ;

h1>Sumw2 ( ) ;

h2>Sumw2 ( ) ;

Float_t mean = 2 0 , sigma = 4 ;

f o r ( I nt _t i = 0 ; i < 1 0 0 0 0 ; i++) {

h1>Fill ( gRandom>Gaus (mean ,sigma ) ) ; / / p ha n b o G au ss

h2>Fill ( gRandom>Landau (mean ,sigma ) ) ; // phan bo Landau

}

/ / Chuan d in h c ua h a i phan bo ve 1

h1>Scale ( 1 . / h1>GetMaximum ( ) ) ;

h2>Scale ( 1 . / h2>GetMaximum ( ) ) ;

/ / V e c a c phan bo

h1>SetLineColor ( kRed ) ;

h2>SetLineColor ( kBlack ) ;

h1>SetLineWidth ( 2 ) ;

h2>SetLineWidth ( 2 ) ;

h1>Draw ( " h i s t o " ) ;

h2>Draw ( " same h i s t o " ) ;

/ / Chon t ho ng s o c ho bang chu g i a i

gStyle>SetOptStat ( 0 ) ; / / an b ang t ho ng t i n h i st o gr a m

le g = new TLegend( 0 . 7 , 0 . 7 , 0 . 9 , 0 . 8 5 ) ; // k ha i b ao b ang c hu g i a ileg>SetTextSize( 0 . 0 4 ) ; / / ch on c o c hu

leg>SetTextColor ( kBlue ) ; // chon mau chu

leg>SetFillColor ( 0 ) ; / / c ho n mau t o

leg>SetBorderSize ( 0 ) ; / / k ho ng v e k hung b a ng c hu g i a i

leg>AddEntry ( h1, " G a u s s i a n " ) ; // d at c hu g i a i cho h is to gr am h 1

leg>AddEntry ( h2, "Landau" ) ; // d at c hu g i a i cho h is to gr am h 2

leg>Draw ( ) ; // v e b ang c hu g i a i

}

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Hnh 5.3: So snh dng phn b Gauss v Landau

5.3 Graph

Graphl mt dng th c to thnh bi hai mng X v Y tng ng nhau. Cphp khai bo graph nh sau:

= new TGraph(n, x, y)Trong n l s im, x v y la hai mng c n im tng ng, hoc

= new TGraph(h) vi h l tn histogram

Mt s lnh lin quan n graph:

(xem thm ti http://root.cern.ch/root/html/TGraph.html)

RemovePoint(i): xa im th i

CompareX(g,i,j), CompareY(g,i,j): so snh gi tr ca hai im th i v j trong

graph g Sort(): sp xp li cc im

V d:(xem Hnh5.4)

{

Double_t x [ 2 0 ] , y[ 2 0 ] ;

I nt _t n = 2 0 ;

f o r ( I nt _t i =0 ; i < n ; i++) {

x [ i ] = co s ( i +0.5) ;

y [ i ] = 3si n ( i2) ;

}

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gr = new TGraph ( n , x , y ) ;

gr>Draw ( "AC" ) ;

}

Hnh 5.4: th phn v d cho graph

5.4 GraphError

GraphErrorl mt dng th c to thnh bi hai mng X v Y tng ng c sais i km. C php khai bo GraphError nh sau:

= new TGraphErrors(n, x, y, ex, ey)

Trong n l s im, x v y la hai mng c n im tng ng, ex v ey l hai mngcha sai s ca x v y

Mt s lnh lin quan n GraphError:

(xem thm ti http://root.cern.ch/root/html/TGraphErrors.html)

GetErrorX(i), GetErrorY(i): sai s theo trc x v y ti bin th i

Apply(f): p dng hm f(x,y) cho tt c cc im

V d:(xem Hnh5.5)

{

I nt _t n = 1 0 ;

Double_t x [ n ] = {0.2 , 0 . 1 , 0 . 3 , 0 . 4 , 0 . 7 , 0 . 8 , 1 . 0 , 1 . 6 , 2 . 4 ,

2 . 7 } ;

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Double_t y [ n ] = { 1 .2 , 2 . 3 , 4 . 0 , 5 . 1 , 7 . 7 , 8 . 7 , 6 . 5 , 4 . 5 , 2 . 7 ,

1.3};

Double_t ex [ n ] = { 0 .0 2 , 0 . 0 3 , 0 . 0 5 , 0 . 0 5 , 0 . 0 7 , 0 . 0 4 , 0 . 0 5 , 0 . 0 6 ,

0 . 0 4 , 0 . 0 1 } ;

Double_t ey [ n ] = { 0. 6 , 0 . 1 , 0 . 8 , 0 . 6 , 0 . 9 , 0 . 7 , 1 . 0 , 0 . 5 , 0 . 5 ,

0 . 2 } ;

gr = new TGraphErrors ( n , x , y , ex, ey ) ;

gr>SetMarkerStyle ( 2 1 ) ;

gr>SetMarkerColor ( 4 ) ;

gr>Draw ( "ALP" ) ;

}

Hnh 5.5: th phn v d cho GraphError

5.5 MultiGraph

MultiGraphto mt tp hp cc th. C php khai bo MultiGraph nh sau: = new TMultiGraph("", "")

Mt s lnh lin quan n MultiGraph:

(xem thm ti http://root.cern.ch/root/html/TMultiGraph.html)

Add(): thm th vo multigraph

Draw(): v cc th

V d:(xem Hnh5.6)

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{

TMultiGraph mg = new TMultiGraph ( ) ;

Int_t n1 = 1 0 , n2 = 1 0 ;Double_t x1[ ] = {0.1 , 0 . 0 5 , 0 . 2 5 , 0 . 3 5 , 0 . 5 ,

0 . 6 1 , 0 . 7 , 0 . 8 5 , 0 . 8 9 , 0 . 9 5 } ;

Double_t y1[ ] = { 1 , 2 . 9 , 5 . 6 , 7 . 4 , 9 , 9 . 6 , 8 . 7 , 6 . 3 , 4 . 5 , 1 } ;

Double_t ex1 [ ] = { . 0 5 , . 1 , . 0 7 , . 0 7 , . 0 4 , . 0 5 , . 0 6 , . 0 7 , . 0 8 , . 0 5 } ;

Double_t ey1 [ ] = { . 8 , . 7 , . 6 , . 5 , . 4 , . 4 , . 5 , . 6 , . 7 , . 8 } ;

TGraphErrors gr 1 = new TGraphErrors ( n1, x1, y1, ex1,ey 1 ) ;

gr1>SetMarkerColor ( kBlue ) ;

gr1>SetMarkerStyle ( 2 1 ) ;

mg>Ad d ( gr 1 ) ;

Float_t x2[ ] = {0 .2 8 , 0 . 0 0 5 , 0 . 1 9 , 0 . 2 9 , 0 . 4 5 ,

0 . 5 6 , 0 . 6 5 , 0 . 8 0 , 0 . 9 0 , 1 . 0 1 } ;

Float_t y2 [ ] = { 2 . 1 , 3 . 8 6 , 7 , 9 , 1 0 , 1 0 . 5 5 , 9 . 6 4 , 7 . 2 6 , 5 . 4 2 , 2 } ;

Float_t ex2 [ ] = { . 0 4 , . 1 2 , . 0 8 , . 0 6 , . 0 5 , . 0 4 , . 0 7 , . 0 6 , . 0 8 , . 0 4 } ;

Float_t ey2 [ ] = { . 6 , . 8 , . 7 , . 4 , . 3 , . 3 , . 4 , . 5 , . 6 , . 7 } ;

TGraphErrors gr 2 = new TGraphErrors ( n2, x2, y2, ex2,ey 2 ) ;

gr2>SetMarkerColor ( kRed ) ;

gr2>SetMarkerStyle ( 2 0 ) ;

mg>Ad d ( gr 2 ) ;

mg>Draw ( "APL" ) ;

}

5.6 Cc ty chnh v th

Khi v th bng lnh Draw(), ta c th s dng cc ty chnh v cc dng thkhc nhau ca cng mt histogram. Bng5.1trnh by mt s ty chnh thng s dngcho cc histogram 1D v 2D.

Mt s ty chnh cho im nh du (marker), ng (line) v ch t mu

(fill)

Chn mu: SetMarkerColor(), SetLineColor(), SetFillColor()

Chn kiu v: SetMarkerStyle(), SetLineStyle(), SetFillStyle()

Chn b dy: SetMarkerWidth(), SetLineWidth()

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Hnh 5.6: th v d cho MultiGraph

Ph lcBtrnh by cc bng k hiu mu, kiu ng v kiu marker c trong ROOT.

V d:(xem Hnh5.7)

{

TH1F h1 = new TH1F ( "h1", "1D Gaus s ian", 1 00 , 1 00 , 1 0 0 ) ;


f o r ( I nt _t i = 0 ; i < 1 0 0 0 0 ; i++) {


}

h1>SetFillColor ( kBlue ) ; // chon mau to mau xanh

h1>SetLineColor ( kRed ) ; / / c ho n mau l i n e mau do

h1>SetLineWidth ( 3 ) ; // c hon b e day l i n e bang 3

h1>Draw ( " h i s t o " ) ;

h1>SetMarkerStyle ( 2 0 ) ; / chon kieu marker 20

h1>SetMarkerColor ( kGreen ) ; / / c ho n mau m a rk er x an h l a

h1>SetMarkerSize ( 1 ) ; / / c ho n k i c h t hu oc m ark er bang 1

h1>Draw ( "s ame p" ) ;

}

Mt s ty chnh cho trc th (axis) tin hnh hiu chnh cc trc th,ta s dng cc lnh GetXaxis(), GetYaxis(), GetZaxis() chn cc trc x,y,z tng

ng. (Xem thm ti http://root.cern.ch/root/htmldoc/TAxis.html) SetTitle(" "): t tiu cho trc th

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Bng 5.1: Cc ty chnh ca lnh Draw() cho cc histogram 1D v 2D (Xem thm tihttp://root.cern.ch/root/html/THistPainter.html)

1D & 2D SAME V trn cng 1 thE V cc thanh sai sHIST V dng histogramTEXT Ghi gi tr ca im trn thLEGO V dng lego c loi b cc ng b nLEGO1 V dng lego c loi b cc mt b nLEGO2 V dng lego c s dng mu hin th gi tr

1D B V biu ctC V ng lm trn qua cc imL V ng ni cc imP V cc im nh duP0 V cc im nh du k c cho cc bin khng c gi trE0 V thanh sai sE1 V thanh sai s c vch ngang vung gc vi thanh sai sE2 V thanh sai s c khung ch nhtE3 V thanh sai s v t phn din tch thanh theo trc tungE4 V thanh sai s v t din tch c lm trnE5 Tng t E3 nhng b qua cc gi tr 0E6 Tng t E4 nhng b qua cc gi tr 0

2D CYL V trn trc ta trPOL V trn trc ta ccSPH V trn trc ta cuPSR V trn trc ta pseudorapidity/phiBOX V dng hpCOL V dng hp c t muCOLZ Tng t nh COL nhng c thm thang muCONT V ng contour (tng t CONT0)CONT0 V ng contour c muCONT1 V ng contour c phn bit kiu ngCONT2 V ng contour vi cng kiu ngCONT3 V ng contour c t muCONT4 V ng contour c s dng mu ca mtCONT5 V ng contour c s dng tam gic DelaunaySURF V dng mtSURF1 V dng mtSURF2 V dng mt c s dng mu hin th gi trSURF3 Tng t SURF, c thm ng contour pha trnSURF4 V dng mt c lm trn (Gouraud shading)SURF5 Tng t SURF3, c ng contour muSCAT V dng chm im

SetRangeUser(a,b): chn khong v t a n b SetTitleSize(),SetTitleFont(),SetTitleOffset(): chn c ch v font ch v

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Hnh 5.7: th phn b ngu nhin dng Gauss 1 chiu

offset cho tiu trn trc

SetLabelSize(), SetLabelFont(): chn c ch v font ch hin th trn trc

V d:(xem Hnh5.8)

{TH1F h1 = new TH1F ( "h1", "1D Gaus s ian", 1 00 , 1 00 , 1 0 0 ) ;


f o r ( I nt _t i = 0 ; i < 1 0 0 0 0 ; i++) {


}

h1>SetTitle ( "Do t h i G a us si a n " ) ; // dat t i eu de

h1>GetXaxis ( )>SetTitle ( "X[m] " ) ; // g ia t r i cua t ru c x

h1>GetYaxis ( )>SetTitle ( "Counts" ) ; // g ia t r i cua t ru c y

h1>GetXaxis ( )>SetRangeUser (50 ,50) ; / / k ho an g v eh1>Draw ( ) ;

}

5.7 Cch to vn bn v biu thc ton hc

Cc on vn bn (text) c a vo trong pad c th c nm trong cc khung c

gi l pave(lp TPaveLabel) hoc l nm t do. Cc on vn bn hin th tiu th hay cc trc c th c khai bo mt cch trc tip. Tt c cc vn bn, cng thc

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Hnh 5.8: V d chnh cc trc cho th

ton hc hin th trong hnh v u l cc i tng thuc lp TTextv tun theo cphp vit vn bn latex (lp TLatex). Ph lcCtrnh by cch vit mt s k hiu latexn gin c s dng trong ROOT.

V d:(xem Hnh5.9)

{

TLatex l ;

l>SetTextAlign ( 1 2 ) ;

l>SetTextSize( 0 . 0 4 ) ;

l>DrawLatex( 0 . 1 , 0 . 8 , "1 ) C(x) = d #s qr t{#fr ac {2}{#lambdaD}}

#int^ {x}_ {0}cos (#fr ac{#pi}{2}t^ {2})dt" ) ;

l>DrawLatex( 0 . 1 , 0 . 6 , "2 ) C(x) = d #s qr t{#fr ac {2}{#lambdaD}}

# i n t ^ { x } c o s ( # f r a c { # p i } { 2 } t ^ { 2 } ) d t " ) ;

l>DrawLatex( 0 . 1 , 0 . 4 , " 3 ) R = | A| ^ {2 } =

#fr a c {1}{2 }(#[]{ # f r a c {1}{2}+C(V)}^{2}+

#[]{#fr ac{1}{2}+ S(V)}^ {2})") ;

l>DrawLatex( 0 . 1 , 0 . 2 , " 4) F( t ) = #sum_{ i=

#in ft y}^{#i nf ty }A( i ) cos #[]{# fr ac { i }{t+ i }}" ) ;

}

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Hnh 5.9: V d cng thc latex

5.8 Graphics Editor

Bn cnh vic hiu chnh cc hnh v bng cu lnh, ROOT cng xy dng cc lp GUI(Graphics User Interface) nhm gip cho vic hiu chnh hnh v c thun tin hn.

khi ng phn Graphics Editor ta c th nhp vo mc View Editornh trongHnh5.10. hiu chnh cho i tng no trong hnh v (canvas, pad, axis,...) ta ch cnnhp vo i tng trn hnh. Cc hiu chnh bng Graph Editor cng tng ngvi cc hiu chnh bng cu lnh.

Ngoi ra, thay v m Graph Editor trc tip, ta c th hiu chnh hnh v bng cch nhpchut phi vo cc i tng cn chnh v chn cc lnh tng ng nh trong Hnh5.11.

5.9 Bi tp

1. Mt sinh vin tin hnh th nghim o h s suy gim ca tia gamma qua hai loivt liu A v B. Bng5.2trnh by s m thu c ng vi cc b dy khc nhauca hai vt liu A v B. Hy tnh h s suy gim ca gamma i vi hai loi vtliu ny v v trn cng 1 th.

2. Mt phn b s liu m phng phn b liu trong phantom nc c chiu bichm tia gamma (phn b trn mt phng kch thc44cm2) c cho tihttp://nmtp.wikispaces.com/file/detail/dose_distribution.txt. Hy v phn bny theo cc dng col,cont,legovsurf.

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Hnh 5.10: Cch chn Graphics Editor

Hnh 5.11: Cch chnh sa th 2

Bng 5.2: S m theo khong cchB dy (cm) 1 2 3 4 5 6 7

A 452 199 94 45 14 5 5

B 904 276 81 30 7 2 4

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3. Mt detector ghi nhn vt ca 1 ht mang in chuyn ng di tc ng cat trng hng theo trc z. Ht chuyn ng trong mt phng xy, cc v tr ctn hiu ghi nhn ht c cho trong file: http://nmtp.wikispaces.com/file/detail/track_hits.txt

Xc nh xung lng ca ht bit cng t trng l B = 1T v in tch caht l |q|= e.Gi : xung lng ngang ca ht c in tch e chuyn ng di tc ng ca t

trng c xc nh theo cng thcpT[GeV] = 0.3 B[T] R[m], vi R l bn

knh qu o chuyn ng ca ht.

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Chng 6

Cc th vin ton hc

6.1 Cc hm ton hc

TMathl lp cha cc hm ton hc c nh ngha sn trong ROOT (xem thm tihttp://root.cern.ch/root/html/TMath.html). Mt s hm thng dng:

Abs(): hm tr tuyt i

Sqrt(): hm khai cn

ASin(), ACos(): cc hmarcsin(),arccos(),...

Gaus(): hm Gaussian

E(), Pi(): cc gi tre,

Ngoi ra, trong ROOT cng c hai th vin ton hc:

Th vin MathCore: cung cp cc lp v hm cho cc tnh ton s, th vin nybao gm cc hm ton hc, thng k v mt s thut ton c bn.

Th vin MathMore: cung cp cc hm v thut ton nng cao da trn nn tngth vin GNU Scientific Library (GSL).

V d:(xem Hnh6.1){

gSystem>Load ( "libMathMore" ) ;

TLegend le g = new TLegend ( 0 . 7 5 , 0 . 7 , 0 . 8 9 , 0 . 8 9 ) ;

i n t n = 5 ;

TF 1 JBessel[ 5 ] ;

f o r(i n t nu = 0 ; nu < n ; nu++)

{

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CHNG 6. CC TH VIN TON HC ng Nguyn Phng

JBessel[ nu ]= new TF 1 ( "J_0", "ROOT: : Math : : c yl _b es se l_ j ( [ 0 ] , x ) ",

0 , 1 0) ;

JBessel[ nu ]>SetParameters ( nu, 0 . ) ;

JBessel[ nu ]>SetTitle ( " " ) ;

JBessel[ nu ]>SetLineStyle (1 ) ;

JBessel[ nu ]>SetLineWidth (3 ) ;

JBessel[ nu ]>SetLineColor ( nu +1);

}

leg>SetFillColor ( 0 ) ;

leg>AddEntry ( JBessel [0]> DrawCopy ( ) , " J _ 0 ( x ) ", " l " ) ;

leg>AddEntry ( JBessel [1]> DrawCopy ( "same" ) , " J _ 1 ( x ) ", " l " ) ;




leg>Draw ( ) ;

}

Hnh 6.1: Cc hm Bessel J

6.2 S ngu nhin

TRandoml lp to s ngu nhin c bn (chu k109

) (xem thm ti http://root.cern.ch/root/html/TRandom.html). Ngoi ra cn c cc lp TRandom1to s ngu nhin da

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trn thut ton RANLUX (chu k 10171), TRandom2da trn thut ton Tausworthe (chuk 1026) vTRandom3da trn thut ton Mersenne Twister (chu k 106000).

Mt s phn b ngu nhin c nh ngha sn trong ROOT:

Exp(X): phn b exp(x/X)

Integer(max): s nguyn ngu nhin t 0 n max1

Gaus(mean,sigma): phn b Gauss

Rndm(): phn b ngu nhin t 0 n 1

Uniform(x): phn b ngu nhin trong khong t 0 n x

Landau(mean,sigma): phn b Landau

Poisson(mean): phn b Poisson

Binomial(n,p): phn b nh thc

BreitWigner(mean,gamma): phn b Breit Wigner

Ngoi ra ta cn c th gieo s ngu nhiu theo mt phn b t nh ngha thng qua lnhGetRandom().

V d:(xem Hnh6.2)

{TH1F h = new TH1F ( "h", " a b s ( s i n ( x ) / x ) ",5 0 ,0 ,10) ;

h>Sumw2 ( ) ;

TF 1 f = new TF 1 ( " f ", " a b s ( s i n ( x ) / x ) ",0 ,10 ) ; // d in h n g hi a ham f

f o r ( I nt _t i = 0 ; i < 1 0 0 0 0 ; i++) {

h>Fill ( f>GetRandom ( ) ) ; / / g i e o nga u n h i en t h eo phan b o ham f

}

h>Draw ( ) ;

}

6.3 Ma trn

xy dng vo thc hin tnh ton ma trn trong ROOT ta c th s dng cclp ma trn c bn nh TMatrixF, TMatrixD, TMatrixT, hoc cc ma trn i xng(TMatrixFSym, TMatrixDSym, TMatrixTSym),... (xem thm ti http://root.cern.ch/root/html/MATH_MATRIX_Index.html).

Mt s lnh dnh cho ma trn:

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Hnh 6.2: Phn b ngu nhin theo hm |sin(x)/x|

Print(): xut ra gi tr ca ma trn

Determinant(): tnh nh thc

Invert(): tnh nh thc

Transpose(): tnh nh thc Plus(a,b): tng hai ma trn

Minus(a,b): hiu hai ma trn

Mult(a,b): tch hai ma trn

V d:Tnh nh thc v ma trn nghch o ca mt ma trn cho trc

{

#include

Double_t x [ ] = { 3 , 4 , 0 , 1 } ;

/ / T ao ma t r a n n k i c h t hu oc 2 x2 t u mang x

TMatrixD n (2 ,2 , x ) ;

/ / Tinh d in h t hu c c ua ma t r an n

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Dinh thuc = 3

2x 2 m at ri x i s a s f ol lo ws

| 0 | 1 |

0 | 0 . 3 3 3 3 1.333

1 | 0 1

V d:Tnh tr ring v vector ring ca ma trn i xng

{

#include

#include

#include

c on st i n t N = 3 ;

/ / T ao mang v o i k i c h t h uo c NN

double e [ NN ] = { 1 , 4 , 5 ,

4 , 2 , 6 ,

5 , 6 , 3 } ;

/ / T ao ma t r a n d o i xun g v o i mang vua t a oTMatrixDSym m ( N , e ) ;

TMatrixDSymEigen me (m ) ;

// Tinh t r i r ie n g va v ec to r r ie ng

TVectorD eigenval = me .GetEigenValues ( ) ;

TMatrixD eigenvec = me .GetEigenVectors ( ) ;

/ / Xuat k e t qu a

m .Print ( ) ;

eigenval.Print ( ) ;

eigenvec.Print ( ) ;}

Kt qu

3x 3 m at ri x i s a s f ol lo ws

| 0 | 1 | 2 |

0 | 1 4 5

1 | 4 2 62 | 5 6 3

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Cross(v): tch hu hng vi vector v

Unit(v): ly vector n v

Angle(v): gc gia hai vector

RotateX(phi), RotateY(phi), RotateZ(phi): quay quanh trc mt gc phi

Rotate(phi,v): quay quanh vector v mt gc phi

V d:Tnh tng hai vector vi lp TVector3

{

TVector3 v1 (1 ,3 ,2) ;

TVector3 v2 (2 , 2 , 0 ) ;

v1 += v2 ;

v1 .Print ( ) ;

}

Kt qu

TVector3 A 3D physics vector ( x , y , z ) = ( 1 . 0 0 0 0 0 0 , 5 . 0 0 0 0 0 0 , 2 . 0 0 0 0 0 0 ) (

rho,theta,ph i ) = ( 5 . 4 7 7 2 2 6 , 6 8 . 5 8 3 2 8 6 , 1 0 1 . 3 0 9 9 3 2 )

V d:Tnh tng hai vector vi lp TVectorD

{

#include

TVectorD v1 ( 2 ) ;

TVectorD v2 ( 2 ) ;

v1 ( 0 ) = 1 ; v1 ( 1 ) = 3 ;

v2 ( 0 ) =2; v2 ( 1 ) = 2 ;

v1 .Ad d ( v2 ) ;

v1 .Print ( ) ;

}

Kt qu

Vector ( 2 ) i s a s f ol lo ws

| 1 |

0 |1

1 | 5

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6.5 Lorentz Vector

TLorentzVectorl vector 4 chiu c xy dng bng cch thm 1 phn t vo trong

TVector3. y l lp vector thng hay c s dng trong cc bi ton ht c bni hi s dng cc php bin i Lorentz, tnh khi lng bt bin,... (xem thm tihttp://root.cern.ch/root/html/TLorentzVector.html).

Mt s lnh dnh cho Lorentz vector:

SetXYZT(): t cc gi tr ta (x,y,z) v thi gian t

SetPxPyPzE(): t cc gi tr xung lng (px,py,pz) v nng lng E

SetPtEtaPhiE(): t cc gi tr xung lng ngang pT, gc , v nng lng E

SetPtEtaPhiM(): t cc gi tr xung lng ngang pT, gc , v khi lng M

Rho(), CosTheta(), Phi(), E(), M(),...: truy xut cc gi tr , cos(), E, M,...

Boost(v): chuyn trc ta theo vector v

V d:Tnh khi lng bt bin ca mt ht c nng lng E v xung lng (px,py,pz)

{

Double_t E = 0 . 5 7 , px = 0 . 1 , py = 0 . 1 , pz = 0 . 2 ;

/ / K ha i b ao mot h at c o n an g l u o ng E va xung l u o ng px , py , p zTLorentzVector particle ( px, py, pz, E ) ;

// Tinh k ho i l uo ng b at b ie n cua h at

cout


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T Lo re n tz Ve c to r b om ba rd ( E , 0 , 0 , E ) ;

// Hat b i a c o k ho i l uo ng m

T Lo re nt zV ec to r t ar ge t ( 0 , 0 , 0 , m ) ;

/ / V e ct o r k h o i t am

T Lo re nt zV ec to r c ms = bombard+target;

TVector3 boost = cm s.BoostVector ( ) ;

// Hat t o i t ro ng he t oa do k ho i tam

bombard.Boost ( boost ) ;

bombard.Print ( ) ;

// Hat b i a t ro n g he t oa do k ho i tam

target.Boost ( boost ) ;

target.Print ( ) ;

}

Kt qu

( x , y , z , t ) = ( 1 . 1 4 5 1 5 9 , 0 . 0 0 0 0 0 0 , 0 . 0 0 0 0 0 0 , 1 . 1 4 5 1 5 9 ) ( P , eta, phi, E )

= ( 1 . 1 4 5 1 5 9 , 0 . 0 0 0 0 0 0 , 0 . 0 0 0 0 0 0 , 1 . 1 4 5 1 5 9 )

( x , y , z , t ) = ( 1 . 1 4 5 1 5 9 , 0 . 0 0 0 0 0 0 , 0 . 0 0 0 0 0 0 , 1 . 4 8 1 5 5 0 ) ( P , eta, phi, E )

= ( 1 . 1 4 5 1 5 9 , 0 . 0 0 0 0 0 0 , 3 . 1 4 1 5 9 3 , 1 . 4 8 1 5 5 0 )

6.6 Bi tp

1. gieo ngu nhin mt phn b f(x)> 0ngi ta c th s dng hai trong nhiuphng php sau:

Phng php hit-and-miss:

Gieo mt cp s ngu nhin (xi, yi)trong khong xmin < xi < xmax v0< yi < max(f(x)).

Nu yi f(xi)th chp nhn gi tr xi.

Nu yi > f(xi)th loi b gi tr xi.

Phng php gii tch: gieo ngu nhin mt gi tr utrong khong 0 < u


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Hy gieo ngu nhin phn b f(x) = 0.05e0.05x vi xtrong khong 0 < x < 100bng c hai phng php.

2. Mt h detector ghi nhn hai ht muon pht ra t phn r ca Z boson. Xung lng

ca hai ht ln lt l: p1x= 5.4 GeV/c, p1y= 42.9 GeV/c, p1z= 32.2 GeV/c, vp2x= 4.6 GeV/c, p2y= -22.9 GeV/c, p2z= -32.2 GeV/c (khi lng ca ht muonc th b qua).H detector c th ghi nhn xung lng ngang (pT= p2x+ p2y) vi phn gii 5%,thnh phn pzc ghi nhn vi phn gii 20%. Hy m phng p ng ca hdetector vi 1000 event v v histogram khi lng bt bin ca h hai ht muon.

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Chng 7

File

7.1 Khai bo file

C php khai bo file nh sau:TFile = new TFile("", option)

hocTFile ("", option)

Mt s ty chnh cho file

NEW: to file mi, trong trng hp file cng tn c tn ti, file mi s khng c

to ra.

CREATE: tng t NEW.

RECREATE: to file mi trong ngay c khi hin dang c file cng tn vi file nhto.

UPDATE: m file c sn, nu cha c th to mi.

READ: m file v c (mc nh).

Mt s lnh cho file (xem thm tihttp://root.cern.ch/root/html/TFile.html)

Close(): ng file

Draw(): duyt cc cu trc ca file

GetSize(): tr v kch thc ca file

ls(): lit k ni dung ca file

Print(): in tt c i tng c trong file

Recover(): phc hi file

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CHNG 7. FILE ng Nguyn Phng

ReOpen(): m li file

Seek(): tm n v tr c th trong file

V d:

root[ 0 ] TFile f = new TFile ( " h i s t o g r a m . r o o t " ) ;

root[ 1 ] f>ls ( ) ;

TFile histogram.root Histograms f o r ROOT c l a s s

TFile histogram.root Histograms f o r ROOT c l a s s

KE Y: TH1F hist1 ; 1 F u nc ti on t o b e f it

KE Y: TH1F hist2 ; 1 A n o th er f un ct io n t o b e f it

root[ 2 ] . q

Mt s c im ca ROOT file

Khi ROOT file c m, n tr thnh th mc hin hnh.

Tt c cc hisotgram v tree s c t ng lu vo file.

Khi file ng, tt c cc histogram, tree, i tng lin quan u s b xa b.

Tt c cc i tng c xut x t TObject u c th c ghi trn file.

7.2 Tree

Trong qu trnh x l, d liu c th c t chc theo nhiu cch khc nhau. Tuy nhin,trong cc trng hp thng thng, d liu c lu di dng tuyn tnh (record) vcui cng c t chc di dng cc bng (table). Tt nhin cch t chc d liu nycng c chp nhn trong ROOT. Cc bng ny c gi l cc n-tuple, ccrecordcgi leventv cc tiu ct c gi l cc bin (variable).

Chng ta c th lu cc n-tupletrong ROOT theo hai cch. Cc th nht l lu theomt chui cc event, y cng l cch lu d liu thng thng. Tuy nhin, khi ngi sdng ch quan tm n mt b s liu nh hn nhiu so vi cu trc d liu c lu thhiu qu x l s khng c cao do phi di chuyn t b s liu ca event ny n bs liu ca event k tip. Do , thay v lu tr theo chui cc event, ROOT s chia tchmi event theo cc bin v xy dng mt tp tin bng cch t cng tt c cc ct. iuny to ra hai u im: th nht, mi ct l mt chui ng nht ca cng mt bin,do s cho kch thc file nh hn nhiu so vi trng hp thng thng. Th hai, khi

ngi s dng ch quan tm n mt vi bin c th ca mi event, thi gian truy xutd liu nh hn nhiu do khng phi qut ton b d liu trong file.

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4 4 0 . 0 7 9 1 2 0 2.322895

5 5 3 . 9 1 1 9 4 1 19.55198

6 3 9 . 5 1 0 5 9 3 33.30006

7 2 9 . 3 9 3 2 9 5 31.64893

8 4 7 . 6 7 3 9 6 5 12.08088

9 4 5 . 7 9 7 2 1 4 1.464032

10 6 0 . 6 0 9 0 2 0 27.04453

11 5 1 . 6 5 3 3 6 9 3.626074

12 3 8 . 6 5 2 2 8 6 4.989183

13 3 8 . 1 7 5 6 4 0 6 5 . 3 2 9 3 9 1

14 3 7 . 5 7 1 5 2 1 6 9 . 9 0 5 8 3 8

15 4 0 . 0 4 8 0 6 1 2.665381

16 5 5 . 4 0 5 3 1 5 1 2 . 8 4 2 2 8 4

17 5 5 . 2 4 6 9 2 1 4 6 . 5 0 2 5 7 4

18 3 8 . 6 3 6 9 0 9 4 . 0 2 3 5 2 8 1

19 3 7 . 0 6 2 3 5 5 6 . 4 4 9 2 5 2 1

20 2 8 . 3 9 7 0 6 4 1 0 . 3 7 0 8 6 3

21 4 0 . 2 2 0 6 4 2 7 . 8 6 2 4 1 8 6

22 2 6 . 7 8 3 8 2 3 6 2 . 3 2 9 8 1 1

23 3 6 . 6 7 6 2 2 7 2 . 5 8 1 8 1 9 3

24 2 8 . 1 9 7 8 4 7 25.71282

Type to c o n ti n ue o r q to qu it ==>

7.2.2 TTree

LpTTreekhc vi lp TNtuple ch l lp TNtuplech gii hn trong vic cha d liudng s trong khi lp TTreec th cha mi loi d liu chng hn nh cc i tng(object) hoc cc mng. C php khai bo Tree nh sau:

TTree = new TTree("", splitlevel)

Mt s lnh dnh cho Tree

CloneTree(): copy tree

Fill(): lu tt c cc branch

AddBranchToCache(), DropBranchFromCache(): thm, loi bbranchtrong tree

GetEntries(): tr v tng s entry

Merge(list): hp nht tt c cc tree c trong list

Show(entry): lit k tt c cc gi tr caleaf trong entry

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Process(): thc thi code i vi mi event

Print(): in ra bng tm tt ni dung ca tree

Scan(): in ra tt c cc entry vt qua selection

StartViewer(): khi ng giao dinTreeViewer

V d:(xem Hnh7.1)

{

T Fi le f ( " 1 1 6 9 4 4 . ro o t " ) ;

TTree t = ( TTree ) t>Ge t ( "HWWTree_e" ) ;

t>StartViewer ( ) ;

f>Close ( ) ;

}

Hnh 7.1: Cu trc ca tree

7.2.3 Cu trc ca tree

Mt tree c th cha cc branch(nhnh), cc branchny c th l cc bin, cc object

hoc bao gm c tree khc. Cui mi branchlun l mt bin, c gi lleaf(l). Thngthng, cc tree u c chia thnh ccbranchkhi c lu vo mt file ROOT. Bi vcu trc tree phc tp hn so vi cu trc bng, nn mc chia tch c th c iu

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chnh ph hp vi nhu cu ca ngi s dng. Hnh 7.2 trnh by cu trc ca mttree.

Cc tree c th c lu tr trn nhiu file khc nhau v c th c ni tip vi nhau

trong qu trnh x l thng qua mt i tng duy nht gi l chain.

Hnh 7.2: Cu trc ca tree

7.3 Cch to v truy xut d liu t file root

7.3.1 Cch to file root

Cc bc to mt file root nh sau:

1. To mt fileVD: TFile *file = new TFile("file.root","RECREATE");

2. To mt treeVD: TTree *tree = new TTree("Tree","Tree");

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Nu mun to tree vi th mc bn trong ta c th lm nh sau:TTree tree("Tree","/folder")

3. Thmbranchvo tree

VD: Event *event = new Event();tree->Branch("EventBranch","Event",&event);

4. Lu d liu vo treeVD: tree->Fill();

5. Lu vo fileVD: file->Write();

V d:

{T Fi le f ( "example . r oo t ", " r e c r e a t e " ) ;

TTree t = new TTree ( " t r e e ", " t r e e " ) ;

Float_t px, py, pz ;

t>Branch ( "px" ,& px, "px/F" ) ;

t>Branch ( "py" ,& py, "py/F" ) ;

t>Branch ( "pz" ,& pz, "pz/F" ) ;

f o r ( I nt _t i =0 ; i Rannor ( px, py ) ;

pz = px px + py py ;

t>Fill ( ) ;

}

t>Write ( ) ;

}

7.3.2 Cch truy xut file root

Cc bc truy xut mt file root nh sau:

1. M mt fileVD: TFile file("file.root");

2. c treeVD: TTree * tree = (TTree*) file->FindObject("tree")

3. To cc bin lu gi liuVD: Float_t a, b, c;

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4. Lin ktbranchvi cc binVD: tree->SetBranchAddress("a", &a)

5. c entry v ly gi tr ca bin

VD: tree->GetEntry(i); cout a endl;V d:(xem Hnh7.3)

{

TFile f = new TFile ( "example . r oo t " ) ;

TTree t = ( TTree ) f>Ge t ( " t r e e " ) ;

Float_t px, py, pz ;

t>SetBranchAddress ( "pz" ,& pz ) ;

TH1F hp z = new TH1F ( "hpz", "pz",1 00 ,0 ,10 ) ;

Long64_t nentries = t>GetEntries ( ) ;

f o r ( Long64_t i =0 ; iGetEntry ( i ) ;

hpz>Fill ( pz ) ;

}

hpz>Draw ( ) ;

}

Hnh 7.3: V d file root

Trong trng hp mun xem nhanh histogram ca mt vi bin, ta c th s dng lnhDraw().

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V d:Cu lnh v histogram ca sqrt(x) vi cc gi tr x>0, histogram c t tn lhisto

tree>Draw ( " s q r t ( x ) >> h i s t ", "x>0" ) ;

Ngoi ra, trong trng hp tree c chia thnh nhiu file, ta c th dng TChain nicc file li. V d:

TChain chain ( " t r e e " ) ;

chain>Ad d ( " f i l e 1 . r o o t " ) ;

chain>Ad d ( " f i l e 2 . r o o t " ) ;

. . .

7.4 X l s liu c cu trc dng tree

Quy trnh x l s liu c cu trc dngtreehocntuplethng thng bao gm ba bcsau

M file s liu, khai bo cc bin, hitogram,...

To vng lp trn tt c cc d liu (entry) cha trong file, tin hnh tnh ton gi

tr, p dng cc ngng ct, lu gi tr vo histogram,... Lu kt qu, biu din kt qu,...

tin hnh x l d liu c cu trc dng treehocntuplecha trong cc file ROOT,vic u tin ta cn lm l to ra mt lp x l (analysis class). B khung sn (skeleton)ca lp ny c to ra thng qua lnh MakeClass().

root [ 0 ] TFile myFile ( " d a t a . r o o t " )

root [ 1 ] tree>MakeClass ( "MyAnalysis" ) // g i a s u d o i t uong t hu oc

l op TTree co t en l a t r e e

Lnh MakeClass()s to ra hai file MyAnalysis.hvMyAnalysis.Ctng ng vi tnca lp m ta mun to ra. File MyAnalysis.hl file header cha cc khai bo cho lpm ta to, trong file ny cng cha danh sch cc bin c trong file ROOT m ta munx l.

V d:MyAnalysis.h

c l a s s MyAnalysis {

p u b l i c :

/ / Con t r o d o i t uo ng t h uo c l o p TTree ha y T Chain

TTree fChain;

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/ / T re e h i e n t a i t r on g TChain

Int_t fCurrent;

/ / C ac b i e n

UInt_t fUniqueID;

UInt_t fBits;

Char_t fType[ 2 0 ] ;

Int_t fNtrack;

Int_t fNseg;

Int_t fNvertex;

UInt_t fFlag;

/ / Cac n ha nh ( b r an c h )

TBranch b_fUniqueID;

TBranch b_fBits;

TBranch b_fType;

TBranch b_fNtrack;

TBranch b_fNseg;

TBranch b_fNvertex;

TBranch b_fFlag;

. . .

MyClass ( TTree tree =0);

~MyClass ( ) ;

I nt _t Cut ( Int_t entry ) ;

I nt _t G et En tr y ( Int_t entry ) ;

I nt _t L oa dT re e ( Int_t entry ) ;

v o i d Init ( TTree tree ) ;

v o i d Loop ( ) ;

Bool_t Notify ( ) ;

v o i d Show ( Int_t entry = 1) ;

} ;

Mt s thnh phn quan trng trong lp ny gm c: fChain: tr titreehaychaingc (ltreehaychainm lp ny c to ra t ).

fCurrent: tr titreehaychainhin ti ang x l, c bit trong trng hp xl nhiutreelin kt li vi nhau qua TChain.

void Init(TTree *tree): khi totree chun b c d liu.

Int_t GetEntry(Int_t entry): c entrytng ng, v d GetEntry(9)s cs kin th 10 trongtree(s kin u tin c ch s l 0).

void Loop(): hm cha cc lnh x l, hm ny s lp trn tt c d liu trongtreehaychainv p cc lnh x l vo tng d liu.

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V d:MyAnalysis.C (trong day quan trong nhat la ham Loop())

v o i d MyAnalysis: : Loop ( ) {

// I n a ROOT s e s si o n , you ca n do :

// Root > . L MyClass .C

// Root > MyClass t

// Root > t . GetEntry ( 1 2 ) ; // F i l l t d at a members w it h e n t ry

number 12

// Root > t . Show () ; // Show v a l u e s o f e n t r y 12

// Root > t . Show (1 6) ; // Read and show v al ue s of e nt r y 16

// Root > t . Loop () ; // Loop on a l l e n t r i e s

//

// This i s t he lo o p s ke le to n where :// j en tr y i s th e g l o ba l e nt r y number in t he c ha in

// i e nt r y i s th e en tr y number in t he c u rr en t Tree

/ / N ot e t h a t t h e a rg um en t t o G et En tr y m ust b e :

// j e n t r y f o r TChain : : GetEntry

/ / i e n t r y f o r T Tre e : : G et En tr y a nd T Bra nch : : G et En tr y

//

// To r ea d on ly s e l ec t ed b r anches , I n se r t s ta te me n ts l i k e :

// METHOD1:

// fChain>SetB r anchSta tus (" " , 0) ; // d i s ab l e a l l b ra nch es// fChain>S e t Br a n ch S t a tu s ( " b ra nc hn am e " , 1 ) ; / / a c t i v a t e

branchname

// METHOD2: re pl ac e l i n e

// fChain>GetEntry ( j e nt r y ) ; // r ea d a l l b ra nch es

//by b_branchname>G et En tr y ( i e n t r y ) ; / / r e a d o n l y t h i s b ra nc h

// gROOT>Res et () ;

i f ( fChain == 0) r e t u r n;

/ Cac k ha i bao v i e t o day /

/ / Tong s o e n t ry t r on g c h a in

Int_t nentries = Int_t ( fChain>GetEntries ( ) ) ;

// Lap t re n t a t ca e nt ry

Int_t nbytes = 0 , nb = 0 ;

f o r ( Int_t jentry =0 ; jentry


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/ / t r o n g t r u o n g h op TChain , 'i e n t r y ' l a s o e nt r y t ro n g f i l e dang

doc

nb = fChain>GetEntry ( jentry ) ; nbytes += nb ;

// i f ( Cut ( i e n t r y ) < 0 ) c o nt i nu e ;

/ Doan c od e x u l y v i e t o day /

}

/ Doan c od e l uu va t r i n h bay k et qua xu l y /

}

FileMyAnalysis.C cha cc ni dung tng ng vi cc hm c khai bo trongMy-Analysis.h. Cc x l s liu u c thc hin trong hm Loop(), cc khai bo v lnhtng ng c t ti cc v tr nh c ch ra trong v d bn trn.

V d:

v o i d An a: : Loop ( ) {

i f ( fChain == 0) r e t u r n;

Int_t nentries = Int_t ( fChain>GetEntries ( ) ) ;

TH1F hist = new TH1F ( " ", " ", 1 00 , 0 , 1 00 00 ) ;

Int_t nbytes = 0 , nb = 0 ;

f o r ( Int_t jentry =0 ; jentryGetEntry ( jentry ) ; nbytes += nb ;

f o r( Int_t itrack =0 ; itracksize ();++itrack ) {

i f( TrackP>at ( itrack ) > 1 00 0)

hist>Fill ( TrackP>at ( itrack ) ) ;}

}

hist>Draw ( ) ;

}

thc thi file x l, ta thc hin nh sau

root [ 0 ] . L MyAnalysis. C

root [ 1 ] MyAnalysis a

root [ 2 ] a .Loop ( )

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7.5 Bi tp

1. B s liu m phng phn b liu trong phantom nc (kch thc 4 4 4cm3)

c chiu bi chm tia gamma c cho ti http://nmtp.wikispaces.com/file/detail/dose_phantom.txt. Hy to mt file root c tn l dose.root, c cha 1 treec tn lDoseDistribution. Lu b s liu ny vo trong root file theo cc bin ta x, y, z.

2. c file root c to ra trong bi tp trc, v cc phn b liu:

Theo trc x, y, z i qua tm ca phantom.

Trn mt phng xy, yz, xz i qua tm ca phantom.

Trn mt phng xy, yz, xz ti bin ca phantom.

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http://nmtp.wikispaces.com/file/detail/dose_phantom.txthttp://nmtp.wikispaces.com/file/detail/dose_phantom.txthttp://nmtp.wikispaces.com/file/detail/dose_phantom.txthttp://nmtp.wikispaces.com/file/detail/dose_phantom.txt


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Li kt

Ti liu ny c bin son vi mc ch cung cp cho ngi c mt ci nhn khi qutcng nhng kin thc cn bn nht trong vic s dng ROOT trong cng vic phn tchv x l s liu. Mc d vn cn rt nhiu ch cha c cp n trong ti liu, tuynhin vi nhng g c trnh by, hi vng cc bn s nm bt c phn no nhng kinthc nn tng ca ROOT t c th tm hiu su hn v chng trnh ny thngqua cc ti liu ph bin trn mng internet. c bit i vi nhng bn c nh hngnghin cu v lnh vc thc nghim ht c bn, y gn nh l mt cng c khng ththiu trong cng vic ca cc bn sau ny.

Mc d rt c gng, nhng do thi gian hn hp nn chc chn ti liu ny vn cnnhiu thiu st v ni dung cng nh hnh thc trnh by. Rt mong nhn c s nggp kin ca cc bn vic bin son ti liu ngy cng tt hn.

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Documents

Hướng dẫn sử dụng ROOT cho hệ điều hành Windows